Multi-layer description model for radon concentration in soil

A theoretical model is proposed to describe some experimental data for radon concentration in soil. The data shows a non-monotonic increase of the radon concentration with the soil depth. The model is based on the general transport equation that includes both diffusion and advection. A multi-layer soil configuration is assumed. Two challenges are faced. The first is that the exact solution of the transport equation is cumbersome to deal with for describing soils with more than two layers. The second is that some approximate solutions may lead to discontinuity between the different layers. In this study an efficient mathematical formulation is suggested that successfully reaches an approximate form which can cope with the two challenges. This formula is much simpler than the exact one, and can easily be applied to include many layers with smooth transition from one layer to the next. The model gives a good fitting with the experimental data and gives important characteristics of radon distribution and transport in soils that require a multi-layer description.